N identical current sources each of emf E and internal resistance r are connected to form a closed loop as shown in figure. The potential difference between points A and B which divides the circuit into n and (N-n) units is

Explanation

(a) Let `epsilon`,R be the emf and internal resistance of a cell. Here N cells are connected in series. Hence current in the circuit is given by
`I = (N epsilon)/(NR) = (epsilon)/(R) = (alpha R)/(R) = alpha`
(b) Potential difference between A and B
`V_(AB) = V_(A) - V_(B) = n epsilon - n (IR)`
`= n (alphaR) - n (E//R) R = n alpha R - n alpha R = 0`